ACTG 323 - Fluconazole (the study drug) is one of the most commonly prescribed drugs to treat thrush and other yeast infections. It is still not known how much fluconazole to give and how often to give it to prevent thrush from coming back in HIV-infected persons who have had thrush in the past. The main purpose of this study is to determine whether it it better to give subjects fluconazole to prevent thrush from coming back, or to wait and treat each episode of thrush whenever it happens. These are the prevention groups that will be studied. The study will also look at: 1) The effect of each strategy on the development of thrush in other places, such as in the esophagus and the vagina, 2) conditions or factors that put HIV-infected persons at risk for developing yeast infections and yeast infections that do not respond to fluconazole, 3) what happens to people who don't respond to treatment with fluconazole, and 4) the effect of each strategy on the quality of subjects' lives.